derivative 10^{8-x^2}

Lösung

ableitung von

1 0^{8 - x^{2}}

- ln (10) \cdot 5^{8 - x^{2}} \cdot 2^{- x^{2} + 9} x

Schritte zur Lösung

\frac{d}{d x} (1 0^{8 - x^{2}})

Wende Exponentenregel an:

a^{b} = e^{b l n (a)}

1 0^{8 - x^{2}} = e^{(8 - x^{2}) l n (10)}

= \frac{d}{d x} (e^{(8 - x^{2}) l n (10)})

Wende die Kettenregel an:

e^{(8 - x^{2}) l n (10)} \frac{d}{d x} ((8 - x^{2}) ln (10))

= e^{(8 - x^{2}) l n (10)} \frac{d}{d x} ((8 - x^{2}) ln (10))

\frac{d}{d x} ((8 - x^{2}) ln (10)) = - 2 ln (10) x

= e^{(8 - x^{2}) l n (10)} (- 2 ln (10) x)

Vereinfache

e^{(8 - x^{2}) l n (10)} (- 2 ln (10) x) : - ln (10) \cdot 5^{8 - x^{2}} \cdot 2^{- x^{2} + 9} x

= - ln (10) \cdot 5^{8 - x^{2}} \cdot 2^{- x^{2} + 9} x

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